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`        find the integral solutions of the equation (1-i)^x=(2)^x`
6 years ago

Sukhendra Reddy Rompally B.Tech Mining Machinery Engg, ISM Dhanbad
93 Points
```										Dear Student,
Taking Log on both sides,u get xlog1/logi = xlog2
U have log1=0 and log2 is not equal to 0,which means x has o be zero
and that is the only integral solution
THANKS
ALL THE BEST
PLZZZ APPROVE MY ANSWER IF YOU LIKE IT
```
6 years ago
Sukhendra Reddy Rompally B.Tech Mining Machinery Engg, ISM Dhanbad
93 Points
```										Dear Student,
Sorry for the wrong reply,i went wrong somewhere...
Anyways,taking Log on both sides,u get xLog(1-i) = x Log2
multiply and divide 1-i by root 2,u get 1-i/2^0.5 = e^-ipie/4
that is x( 0.5Log2 - i22/28 ) = xLog2
that is xLog2 = -i22/28 and x=0 are the solutions
clearly,x is imaginary if the 1st eqn is true,hence,x=0 is the only integral solution

THANKS
ALL THE BEST
PLZZZ APPROVE MY ASNWER IF YOU LIKE IT
```
6 years ago
mycroft holmes
271 Points
```
```
6 years ago
Vishva vivek singh
13 Points
```										(1-i)^x=2^x1-iComplex number is of the from x+iyWhere x=1             Y=-1I 1-i l=√x^2+y^2l 1-i l=√2 Hence  l 1-i l^x=2^x  Putting value     (√2)^x=2^x     √2^x=(√2×√2)^x    √2^x=(√2)^2x  Comparing powers           x=2x           x-2x=0            -x=0              X=0
```
2 months ago
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